In 1950, he enlisted in the United States Coast Guard and after serving in New York City, moved out to California. It was there that he met bodybuilder Millard Williamson, who encouraged him to begin weight training.

At 160 pounds and at the age of 33, Corney entered and won his first contest in 1967, the Mr. Fremont, held in Northern California. His wins the following year included Mr. Heart of California, Mr. Northern California and Mr. Golden West.

He continued to climb the bodybuilding ladder with impressive wins at the 1970 Iron Man, the 1971 AAU Mr. California, the 1971 IFBB Mr. USA, the 1972 IFBB Mr. America and the 1972 IFBB Mr. Universe that was held in Baghdad, Iraq.

Corney achieved even broader public recognition as a result of his appearance in both the book and movie versions of Pumping Iron. He was pictured on the cover of the book and on the posters for the movie.

In 1994, Corney returned to competition. He won the 60+ division of the Masters Olympia in both 1994 and 1995, placed 11th overall in 1996 and took second in the 60+ division in 1997. He also competed in 1998 in the only Masters event ever to be held at the Arnold Schwarzenegger Classic.

Corney remains very active in the sport to this day. In 1999, he suffered a heart attack while undergoing shoulder replacement surgery. A blood thinning medication that was given to him to treat the heart attack caused him to suffer two strokes. After a short period in a coma and some time using a wheelchair, Corney fought his way back to health.